(Received September 5, 1989; revised October 22, 1990)
Abstract. Let U and V be independent random variables with continuous density function on the interval (0,1). We describe families of functions g for which uniformity of U and V is equivalent to uniformity of g(U,V) on (0,1). These results are used to prescribe methods for improving the quality of pseudo-random number generators by making them closer in distribution to the U(0,1) distribution.
Key words and phrases: Characterization of uniform distribution, independence, pseudo-random number generator, fractional sum.